a game about sherlock holmes?

First off, I'm not a lawyer, however, I believe that depends on where you live. In many countries Sherlock Holmes is old enough to be in the public domain. For example, it seems that in the United States, Sherlock Holmes still is under copyright, but in Canada he is not.

Moving this to Business/Law.

Albot, a lawyer can help you determine whether or not Sherlock Holmes is "free and clear" - but you can expect a legal response from a number of people, even movie studios.
You can't go into business without a lawyer's advice.
For more on the topic of using IP you did not create, this article might be enlightening.

Apparently there is a lot of confusion on the matter.

Also worth keeping in mind that regardless of the copyright/lack-therof to Arthur Conan Doyle's original books, there are many derived works (such as the recently released film adaptation), which are very much a going concern. IANAL, but you may need to be careful about infringing on subtleties of those recent works as well.